How To Find P Hat With Confidence Interval

Stats: Estimating the Proportion

You are estimating the population proportion, p.

All estimation done here is based on the fact that the normal tin be used to approximate the binomial distribution when np and nq are both at least 5. Thus, the p that were talking about is the probability of success on a single trial from the binomial experiments.

Recall:

The best point estimate for p is p hat, the sample proportion: p hat = x / n

If the formula for z is divided past n in both the numerator and the denominator, then the formula for z becomes:

Solving this for p to come up with a confidence interval, gives the maximum error of the estimate as: .

This is not, however, the formula that we will utilize. The trouble with estimation is that you don't know the value of the parameter (in this example p), so you can't use it to estimate itself - if you knew it, so there would exist no problem to work out. So we will replace the parameter by the statistic in the formula for the maximum mistake of the judge.

The maximum error of the judge is given by the formula for Due east shown. The Z here is the z-score obtained from the normal tabular array, or the bottom of the t-table as explained in the introduction to estimation. The z-score is a cistron of the level of confidence, so you may get in the addiction of writing it next to the level of conviction.

When you lot're computing East, I suggest that you notice the sample proportion, p hat, and salvage it to P on the calculator. This manner, you tin can discover q as (1-p). Practise Not round the value for p chapeau and apply the rounded value in the calculations. This will lead to error. One time yous take computed East, I propose you lot save it to the memory on your calculator. On the TI-82, a skilful choice would exist the letter E. The reason for this is that the limits for the confidence interval are at present constitute by subtracting and calculation the maximum error of the estimate from/to the sample proportion.